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3 years ago

Volume = 4,410 yd 30 yd radius =

Mathematics

1 answer:

Y_Kistochka [10]3 years ago

8 0

Answer:

Radius = 11.85yd

Step-by-step explanation:

Volume of a Cone formula: V = πr²(h/3)

We know that;

V = Volume

r = radius

π = pi (this is a sign located on your calculator)

h = height

We are given that;

V = 4,410

r = unknown

h = 30

Let's substitute the values in:

=> V = πr²(h/3)

=> 4,410 = πr²(30/3)

=> 4,410 = πr²(10)

=> 4,410 / 10 = πr²

=> 441 = πr²

=> 441 / π = r²

=> 140.37 = r²

=> $\sqrt{140.37}$ = r

=> 11.85 = r

Therefore, <u>the radius of the cone = 11.85yd</u>

Hope this helps!

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Which of the following numbers could be the sides of a right triangle. A)8,15,17. B)6,8,12 C)9,11,21 D)4,13,16

ArbitrLikvidat [17]

Answer:

A) 8, 15, 17.

Step-by-step explanation:

Right triangle obey the Pythagorean theorem. Thus, we choose the two smaller numbers (being the cathetus) and if after applying the P. Theorem we get the biggest of each option (the hypotenuse) that means that those numbers could be the sides of a right triangle.

The Pythagorean theorem states that: $a^2+b^2=c^2$

Thus:

$\sqrt{a^2+b^2}=c$

Option A:

$\sqrt{8^2+15^2}=17$ → 17 = 17 OK!

Option B:

$\sqrt{6^2+8^2} = 10$ → 10 ≠ 12 NO

Option C:

$\sqrt{9^2+11^2} = [tex]\sqrt{202}$ [/tex] → $\sqrt{202}$ ≠ 21 NO

Option D:

$\sqrt{4^2+13^2} = \sqrt{185}$ → $\sqrt{185}$ ≠ 16 NO

3 0

3 years ago

The sum of two consecutive integers is 65. what are the two integers? show steps please.

Gnoma [55]

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to find the two integers, given that they are consecutive, and their sum is 65.

$\triangle~\fbox{\bf{KEY:}}$

Consecutive integers are right next to each other, like 12 and 13. or 65 and 66.

Let the first integer be x, and let the second integer be x+1.

Their sum is 65. Let's set up our equation:

$\longmapsto\sf{x+x+1=65}$

Combine like terms:

$\longmapsto\sf{2x+1=65}$

Subtract 1 from both sides of the equal sign:

$\longmapsto\sf{2x=64}$

Divide both sides by 2:

$\longmapsto\sf{x=32}$

To find the second integer, subtract the first integer from the sum of the two integers:

$\longmapsto\pmb{65-32}$

$\longmapsto\pmb{33}$

The integers are: 33 and 32.

Hope it helps you out! :D

Ask in comments if any queries arise.

#StudyWithBrainly

~Just a smiley person helping fellow students :)

7 0

2 years ago

Is PRB congruent to QSB? Justify your answer.

Serhud [2]

Answer:

When looking at this model, and asking yourself the question, is PRB congruent to QSB? PRB is in fact congruent to QSB. Congruent means that two figures have the same shape/size, no matter if it's mirrioring or not it is congruent. In this image, PRB is one shape, and QSB is another. They have the exact same points and they're also the same shape, but one is flipped the right side up. It was also stated PQ and RS bisect eachother at point B, <p is congruent to <Q, and <R is congruent to <S proving all these connections make this figure conguent.

Step-by-step explanation:

8 0

3 years ago

A hairdryer transfers 36,000J in one minute, what is the power rating of the hairdryer?

Verdich [7]

Answer:

1. 600 watts

2. 35640 J

3. 55%

4. 20 J

5. The cost of running the fire is 8p.

Step-by-step explanation:

1. Energy = 36 000 J , t = 1 minute = 60 seconds

Power = $\frac{energy}{time}$

= $\frac{36000}{60}$

= 600 watts

2. Power = $\frac{work done}{time}$

⇒ work done = Power × time

= 99 × 360

= 35640 J

3. Efficiency = (Output / Input) × 100

= $\frac{55}{100}$ × 100

= 55%

4. Work done = Force × distance

= 5 × 4

= 20 J

5. Given that 1 KWh cost 2p, Power = 4 KW and time = 4 hours.

Power = $\frac{energy}{time}$

Energy = Power × time

= 4 × 4

= 16 KWh

The cost of running the fire = $\frac{16}{2}$

= 8p

3 0

3 years ago

.A bag contains 3 red checkers and 5 black checkers. A checker is selected, kept out of the bag, and then another checker is sel

cupoosta [38]

Answer: 15 / 56

Step-by-step explanation:

Number of red checkers = 3

Number of black checkers = 5

Total number of checkers = 8

P(black, then red) = 5/8 × 3/7 = 15/56

We should note that the probability to pick a black checker first will be 5 out of 8. Then, there'll be 7 checkers left and the probability to pick a res checker will be 3/7. We then multiply the probabality of each together.

5 0

3 years ago